Basic Math Examples

$\frac{7}{9 p^{2} + q} \div \frac{21}{18 p^{2} + 2 q}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{7}{9 p^{2} + q} \cdot \frac{18 p^{2} + 2 q}{21}$

Step 2

Cancel the common factor of $7$ .

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Step 2.1

Factor $7$ out of $21$ .

$\frac{7}{9 p^{2} + q} \cdot \frac{18 p^{2} + 2 q}{7 (3)}$

Step 2.2

Cancel the common factor.

$\frac{7}{9 p^{2} + q} \cdot \frac{18 p^{2} + 2 q}{7 \cdot 3}$

Step 2.3

Rewrite the expression.

$\frac{1}{9 p^{2} + q} \cdot \frac{18 p^{2} + 2 q}{3}$

Step 3

Multiply $\frac{1}{9 p^{2} + q}$ by $\frac{18 p^{2} + 2 q}{3}$ .

$\frac{18 p^{2} + 2 q}{(9 p^{2} + q) \cdot 3}$

Step 4

Factor $2$ out of $18 p^{2} + 2 q$ .

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Step 4.1

Factor $2$ out of $18 p^{2}$ .

$\frac{2 (9 p^{2}) + 2 q}{(9 p^{2} + q) \cdot 3}$

Step 4.2

Factor $2$ out of $2 q$ .

$\frac{2 (9 p^{2}) + 2 (q)}{(9 p^{2} + q) \cdot 3}$

Step 4.3

Factor $2$ out of $2 (9 p^{2}) + 2 (q)$ .

$\frac{2 (9 p^{2} + q)}{(9 p^{2} + q) \cdot 3}$

Step 5

Cancel the common factor of $9 p^{2} + q$ .

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Step 5.1

Cancel the common factor.

$\frac{2 (9 p^{2} + q)}{(9 p^{2} + q) \cdot 3}$

Step 5.2

Rewrite the expression.

$\frac{2}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{3}$

Decimal Form:

$0.\overline{6}$